IPMAT Indore 2023 · Quantitative Ability · Question 7

IPMAT Indore 2023 previous year question on Simple Interest and Compound Interest, with the answer and a step-by-step solution.

Simple Interest and Compound InterestArithmeticType in the answer (TITA)Medium

Assume it is the beginning of the year today. Ankita will earn ₹10,000 at the end of the year which she plans to invest in a bank deposit immediately at a fixed simple interest of 0.5% per annum. Her yearly income will increase by ₹10,000 every year and the fixed simple interest offered by the bank on new deposits will also increase by 0.5% per annum every year. If Ankita continues to invest all her yearly income in new bank deposits at the end of each year, the total interest earned by her in ₹ for five years from today will be _____

Answer & solution

Answer: 2500

Step 1 — lay out the five deposits. Each deposit is made at the end of the year it is earned, so a deposit made at the end of year k only earns interest for the remaining 5-k years.

End of year	Amount deposited	Rate	Years it earns	Interest
1	₹10,000	0.5%	4	10000\times 0.005\times 4=200
2	₹20,000	1.0%	3	20000\times 0.010\times 3=600
3	₹30,000	1.5%	2	30000\times 0.015\times 2=900
4	₹40,000	2.0%	1	40000\times 0.020\times 1=800
5	₹50,000	2.5%	0	0

Step 2 — add.

200+600+900+800+0=2500

Note on the fifth deposit. It is made at the very end of the five-year window, so it has had no time to earn anything. Including it is the single commonest error here.

Answer: ₹2500

Shortcut. Each line is 10000k\times 0.005k\times \left( 5-k \right) — spot the pattern and factor.

\text{Interest}=50\sum_{k=1}^{5}{{k}^{2}}\left( 5-k \right)=50\left[ 1\left( 4 \right)+4\left( 3 \right)+9\left( 2 \right)+16\left( 1 \right)+25\left( 0 \right) \right]

=50\,\left( 4+12+18+16+0 \right)=50\times 50=2500

Two traps, both about timing: the deposit is made at the end of each year (so year-1 money earns for 4 years, not 5), and the final deposit earns nothing. Draw the timeline before computing — the arithmetic itself is trivial once the years are right.

IPMAT Indore 2023 · Quantitative Ability · Question 7

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